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A301560
Matching number of the n-odd graph.
2
0, 1, 5, 17, 63, 231, 858, 3217, 12155, 46189, 176358, 676039, 2600150, 10029150, 38779380, 150270097, 583401555, 2268783825, 8836315950, 34461632205, 134564468610, 526024740930, 2058357681900, 8061900920775, 31602651609438, 123979633237026, 486734856412028
OFFSET
1,3
COMMENTS
The n-odd graph is known to be Hamiltonian for 4 <= n <= 14. Hamiltonian graphs always have a matching with at most one unmatched vertex. - Andrew Howroyd, Mar 23 2018 [Now known for all n >= 4. - Pontus von Brömssen, May 01 2020]
LINKS
T. Mütze, J. Nummenpalo, B. Walczak, Sparse Kneser graphs are Hamiltonian, arXiv:1711.01636, [math.CO], 2017.
Eric Weisstein's World of Mathematics, Independent Edge Set
Eric Weisstein's World of Mathematics, Matching Number
Eric Weisstein's World of Mathematics, Odd Graph
Wikipedia, Odd Graph
FORMULA
a(n) = floor(binomial(2*n - 1, n - 1)/2).
CROSSREFS
Cf. A301557.
Sequence in context: A146444 A128073 A051736 * A099528 A149667 A149668
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Mar 23 2018
EXTENSIONS
a(8)-a(14) from Andrew Howroyd, Mar 23 2018
More terms from Pontus von Brömssen, May 01 2020
STATUS
approved